Notes

No explicit tables of primes appear to have survived from antiquity, but it seems likely that all primes up to somewhere between 5000 and 10000 were known. (In 348 BC, Plato mentioned divisors of 5040, and by 100 AD there is evidence that the fifth perfect number was known, requiring the knowledge that 8191 is prime.) In 1202 Leonardo Fibonacci explicitly gave as an example a list of primes up to 100. And by the mid-1600s there were printed tables of primes up to 100,000, containing as much data as in plots (c) and (d). In the 1700s and 1800s many tables of number factorizations were constructed; by the 1770s there was a table up to 2 million, and by the 1860s up to 100 million. A table of primes up to a trillion could now be generated fairly easily with current computer technology—though for most purposes computation of specific primes is more useful.